“E agora, cinco?”: uma história virtual do conceito para o ensino da tangente no ensino médio

Abstract

This study aims to analyze the potential contributions of an intentional organization of teaching and the development of a pedagogical proposal on the concept of tangent, grounded in the perspective of the Logical-Historical Movement of the Concept and the assumptions of the Guiding Teaching Activity (GTA). It is based on the understanding that mathematics teaching should enable students to access the historical conditions that gave rise to mathematical concepts, fostering the development of theoretical thinking. The research is characterized as qualitative and was developed through the elaboration and implementation of a Learning Triggering Situation (LTS) that addressed historical elements related to the emergence of the concept of tangent. The activity was organized to engage students through a Virtual History of the Concept, designed to highlight the need for the concept of tangent and enable the investigation of its conceptual connections. For the analysis of the empirical material, two analytical axes were established: the understanding of the historical need for the concept of tangent and the identification of its conceptual connections and students’ appropriation of the concept. The results of this research indicate that articulating the study of the Logical-Historical Movement of concepts with the organization of teaching through the Guiding Teaching Activity constitutes a promising approach to teaching trigonometry in the school context, as it enables students to understand the conditions that gave rise to mathematical concepts and fosters an understanding of the conceptual relationships that structure them.